Because they don't really want to sign him long term, but they don't want a fan backlash over not doing so. It's working, because the newly created narrative (i. e. Baltimore tried to resign him at a large figure and it was rejected) makes him look greedy and diminishes him in the eyes of fans, thereby circumventing any backlash.

The Orioles and Mark Trumbo, who was acquired last month in a trade with Seattle, avoided arbitration by agreeing to a $9.15 million deal. If you're keeping score at home, that's $12.85 million less than the annual value of the deal that the O's offered to Chris Davis, whom Trumbo may end up replacing at first base.